Until you get burned a few times by having the TDY cancelled last minute by the Guard Bureau (after you've taken military leave) due to lack of funds, cancelled by the Sq due lack of interest from other crewmembers, or cancelled by MX for broken aircraft. Then you sit around the Sq all week trying to recoup a fraction of your lost airline pay by logging doubles doing CBTs and OPRs if the network is up. I sure hope I don't sound bitter.

While the Guard is better, it is not a solution. The Guard is also deteriorating. It's become Active Duty Lite. However, in the Guard, when people get pissed, they simply don't show up. Try getting anything done on a base with poor morale. This is a very recent change.
I cleaned out a desk drawer the other day an on top was a document that referenced Air Force Basic Doctrine: Centralized Control, Decentralized Execution.
I thought, Big AF is applying this doctrine not to war fighting, but nearly every aspect of the organization. Many of the daily stressors that I hear about in the squadron pertain, in a very large part, to the ceding of control and authority to "data collection" organizations off base. Finance, Persco, Comm... I went down to the Comm Sq last week to raise hell. I sat down with a TSgt and just asked why everything seemed broken. "Lack of manpower, lack of funds, lack of authority to fix anything, higher level organizations do not respond." It was the same when I stormed over to Finance demanding answers recently. My anger turned to apathy when, through conversation, I realized it really wasn't all their fault and there was little they could do, even if my issue became their full time job. It's the same shit everywhere I go on base.
People want meaning in their work that comes through giving our people the means, flexibility, and responsibility to make progress. Nearly all of that has been removed and given to central authorities. The production order comes down from on high and you merely execute. We've all been relegated to double-shift factory work and few find satisfaction in that.
Trying to work through this and checking myself for both pessimism and optimism, and allowing only realism - there's no way to untangle this mess without a comprehensive overhaul that likely will not happen until the most dire of circumstances.

Sounds like the Reserve recruiter won’t work with the applicant if the recruiter knows the applicant is simultaneously applying for Guard positions.
He’s a recruiter. He’s going to tell you want he needs to keep you on the hook. Do the same.

Sure. I normally start with my company employee travel website first and that works 80% of the time.
To find routes, I use passrider.com, flightlookup.com, rome2rio.com, flightconnections.com, expedia, kayak.com, etc.
Apps: Flightboard for "right now" at the airport, StaffTraveler, and FlightAware.
For international, myid90travel.com will give you a rough estimate of available seats, but I think you need a company provided account.
To check specific loads and other questions, I normally just call the airline. Airline websites normally display seats sold, but don't show standbys.
American Airlines Non-Rev: 1-800 933-5922
United Airlines Non-Rev: 1-800-359-3727
UPS Jumpseat: 1-502-359-1437
Yesterday, I got caught up in the mess around Chicago. Talked the company into releasing me from my deadheads early and had to get creative to get home. Passrider and flightboard got me home 18 hours early with one connection between United and Delta with near zero ground time.

Personally, I think travel is a chore and I treat it as such. I like free stuff so I'll make a list of options to get from A to B with the fam on Non=Rev. Prioritize the list according to seat availability, travel time, and number of stops. I keep a whole category of non-rev apps, websites, and 1-800 numbers on my phone. If I can save a few grand by Non-revving the entire family to Paris, that means better hotels, restaurants, experiences.
It can be challenging, but there's always a way. That said, sometimes it's not worth the effort, but I'm more of a cheap bastard than most so I'll work for it.
Always, always, ask the gate agent if they prefer Starbucks or Dunkin.

The Air Force has a pilot shortage. The AFPC person answering the phone/emails does not have a pilot shortage. It makes perfect sense for them to wave a magic wand and make a fully qualified Guard guy an Active Duty pilot, but you're one guy in a gray area for which a process either doesn't exist, is used so little no one knows how, or is so complicated that the effort can't be expended.
Are you aware of all the long term AD orders available around the world? If your unit is willing to allow you to become a free-agent, the possibilities are endless if you dig for them.